Re: Generalized eigenspace

Thank u so much for the 1st answer. It really2 helps.
For the second question, I mean how can we be sure that a generalized eigenspace W has the same dimension as the algebra multiplicity of the eigenvalue,lambda?

Re: Generalized eigenspace

Every matrix satisfies its own characteristic equation. That is, if the characteristic equation for matrix A is then (A- aI)^nv= 0 for every v. It might happen that there are n independent eigenvectors in which case the "eigenspace" has dimension n. If not, if the eigenspace has dimension m< n, for v NOT in that eigenspace, we must have (A- aI)^(n-m)v= 0 so that v is a "generalized" eigen value.